Finite Volume Model for Nonlevel Basin Irrigation
Publication: Journal of Irrigation and Drainage Engineering
Volume 127, Issue 4
Abstract
A finite volume model for unsteady, two-dimensional, shallow water flow is developed and applied to simulate the advance and infiltration of an irrigation wave in two-dimensional basins of complex topography. The fluxes are computed with Roe's approximate Riemann solver and the monotone upstream scheme for conservation laws is used in conjunction with predictor-corrector time-stepping to provide a second-order accurate solution. Flux-limiting is implemented to eliminate spurious oscillations and the model incorporates an efficient and robust scheme to capture the wetting and drying of the soil. Model predictions are compared with experimental data for one- and two-dimensional problems involving rough, impermeable, and permeable beds, including a poorly leveled basin.
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References
1.
Akanbi, A. A., and Katopodes, N. D. (1988). “Model for flood propagation on initially dry land.”J. Hydr. Engrg., ASCE, 114(7), 689–706.
2.
Al-Tamimi, A. H. J. ( 1995). “Two-dimensional transient flow in non-level basins.” PhD dissertation, Dept. of Agric. and Biosys. Engrg., University of Arizona, Tucson, Ariz.
3.
Ambrosi, D. ( 1995). “Approximation of shallow water equations by Roe's Riemann solver.” Int. J. Numer. Methods in Fluids, 20, 157–168.
4.
Bermudez, A., and Vazquez, M. E. ( 1994). “Upwind methods for hyperbolic conservation laws with source terms.” Comp. and Fluids, 23, 1049–1071.
5.
Bradford, S. F., and Katopodes, N. D. (1998). “Nonhydrostatic model for surface irrigation.”J. Irrig. and Drain. Engrg., ASCE, 124(4), 200–212.
6.
Bradford, S. F., and Katopodes, N. D. (1999). “Hydrodynamics of turbid underflows. I: Formulation and numerical analysis.”J. Hydr. Engrg., ASCE, 125(10), 1006–1015.
7.
Bradford, S. F., and Sanders, B. F. (2001). “Finite volume model for shallow water flooding and drying of arbitrary topography.”J. Hydr. Engrg., ASCE, in press.
8.
Casulli, V., and Cheng, R. T. ( 1992). “Semi-implicit finite difference methods for three-dimensional shallow water flow.” Int. J. Numer. Methods in Fluids, 15, 629–648.
9.
Clemmens, A. J. ( 1981). “Evaluation of infiltration measurements for border irrigation.” Agric. Water Mgmt., 3, 251–267.
10.
Dodd, N. (1998). “Numerical model of wave run-up, overtopping, and regeneration.”J. Wtrwy., Port, Coast., and Oc. Engrg., ASCE, 124(2), 73–81.
11.
Fraccarollo, L., and Toro, E. F. (1995). “Experimental and numerical assessment of the shallow water model for two-dimensional dam-break type problems.”J. Hydr. Res., 33, 843–864.
12.
Hirsch, C. ( 1990). Numerical computation of internal and external flows, Wiley, New York.
13.
Ho, D. V., and Meyer, R. E. ( 1962). “Climb of a bore on beach.” J. Fluid Mech., 14, 305–318.
14.
Hughes, T. J. R. ( 1987). The finite element method, Prentice-Hall, Englewood Cliffs, N.J.
15.
Katopodes, N. D. (1982). “On zero-inertia and kinematic waves.”J. Hydr. Div., ASCE, 108(11), 1380–1387.
16.
Katopodes, N., and Schamber, D. R. (1983). “Applicability of dam-break flood wave models.”J. Hydr. Engrg., ASCE, 109(5), 702–721.
17.
Katopodes, N. D., and Strelkoff, T. (1977). “Dimensionless solutions of border-irrigation advance.”J. Irrig. and Drain. Div., ASCE, 103(4), 401–417.
18.
Katopodes, N., and Strelkoff, T. (1978). “Computing two-dimensional dam-break flood waves.”J. Hydr. Div., ASCE, 104(9), 1269–1288.
19.
Kawahara, M., and Umetsu, T. ( 1986). “Finite element method for moving boundary problems in river flow.” Int. J. Numer. Methods in Fluids, 6, 365–386.
20.
Keller, H. G., Levine, D. A., and Whitham, G. B. ( 1960). “Motion of a bore over a sloping beach.” J. Fluid Mech., 7, 302–316.
21.
Lal, A. M. W. (1998). “Weighted implicit finite-volume model for overland flow.”J. Hydr. Engrg., ASCE, 124(9), 941–950.
22.
Liu, P. L. F., Cho, Y., Briggs, M. J., Kanoglu, U., and Synolakis, C. E. ( 1995). “Runup of solitary waves on a circular island.” J. Fluid Mech., 302, 259–285.
23.
Madsen, P. A., Sorensen, O. R., and Schaffer, H. A. ( 1997). “Surf zone dynamics simulated by a Boussinesq type model. Part I. model description and cross-shore motion of regular waves.” Coast. Engrg., 32, 255–287.
24.
Nujić, M. (1995). “Efficient implementation of non-oscillatory schemes for the computation of free-surface flows.”J. Hydr. Res., 33, 101–111.
25.
Okamoto, T., Kawahara, M., Ioki, N., and Nagaoka, H. ( 1992). “Two-dimensional wave run-up analysis by selective lumping finite element method.” Int. J. Numer. Methods in Fluids, 14, 1219–1243.
26.
Playán, E., Walker, W. R., and Merkley, G. P. (1994). “Two-dimensional simulation of basin irrigation. I: Theory,”J. Irrig. and Drain. Engrg., ASCE, 120(5), 837–856.
27.
Roe, P. L. ( 1981). “Approximate Riemann solvers, parameter vectors, and difference schemes.” J. Computational Physics, 43, 357–372.
28.
Sielecki, A., and Wurtele, M. G. ( 1970). “The numerical integration of the nonlinear shallow-water equations with sloping boundaries.” J. Computational Physics, 6, 219–236.
29.
Stockstill, R. L., Berger, R. C., and Nece, R. E. (1997). “Two-dimensional flow model for trapezoidal high-velocity channels.”J. Hydr. Engrg., ASCE, 123(10), 844–852.
30.
Strelkoff, T., and Katopodes, N. D. (1977). “Border-irrigation hydraulics with zero inertia.”J. Irrig. and Drain. Div., ASCE, 103(3), 325–342.
31.
Sweby, P. K. ( 1984). “High resolution schemes using flux limiters for hyperbolic conservation laws.” SIAM J. of Numer. Anal., 21, 995–1011.
32.
Titov, V. V., and Synolakis, C. E. (1995). “Modeling of breaking and nonbreaking long-wave evolution and runup using VTCS-2.”J. Wtrwy., Port, Coast., and Oc. Engrg., ASCE, 121(6), 308–316.
33.
Tisdale, T. S., Scarlatos, P. D., and Hamrick, J. M. (1998). “Streamline upwind finite-element method for overland flow.”J. Hydr. Engrg., ASCE, 124(4), 350–357.
34.
Tucciarelli, T., and Termini, D. (2000). “Finite-element modeling of floodplain flow.”J. Hydr. Engrg., ASCE, 126(6), 416–424.
35.
Van Leer, B. ( 1979). “Towards the ultimate conservative difference scheme. V. A second order sequel to Godunov's method.” J. Computational Physics, 32, 101–136.
36.
Van Leer, B., Lee, W. T., and Powell, K. G. ( 1989). “Sonic point capturing.” AIAA 9th Computational Fluid Dynamics Conf., Buffalo, N.Y.
37.
Wurjanto, A., and Kobayashi, N. (1993). “Irregular wave reflection and runup on permeable slopes.”J. Wtrwy., Port, Coast., and Oc. Engrg., ASCE, 119(5), 537–557.
38.
Zhang, W., and Cundy, T. W. ( 1989). “Modeling of two-dimensional overland flow.” Water Resour. Res., 25, 2019–2035.
39.
Zhao, D. H., Shen, H. W., Tabios, G. Q., III, Lai, J. S., and Tan, W. Y. (1994). “Finite-volume two-dimensional unsteady-flow model for river basins.”J. Hydr. Engrg., ASCE, 120(7), 863–883.
Information & Authors
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Published In
Journal of Irrigation and Drainage Engineering
Volume 127 • Issue 4 • August 2001
Pages: 216 - 223
History
Received: Oct 27, 2000
Published online: Aug 1, 2001
Published in print: Aug 2001
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